JPH03278002A - Optical element and optical pickup device using the same - Google Patents

Abstract

PURPOSE:To obtain the optical element having two functions; a lens function and another optical function, by forming synthetic grating patterns constituted of two kinds of the grating patterns which vary from each other and are superposed on each other on a substrate. CONSTITUTION:The synthetic grating pattern constituted of two kinds of the grating patterns which vary from each other and are superposed on each other are formed on the substrate 10. The gratings are obtd. by a relief type (or corrugation type) which generates the diffraction of light by the projecting lines and recessed grooves on the surface of the substrate 10 or a distributed index type which generates the diffraction of light by a change in the refractive index of the substrate. The optical element having the two functions; a lens function and another optical function, is obtd. in this way.

Description

DETAILED DESCRIPTION OF THE INVENTION Technical Field of the Invention The present invention relates to an optical element and an optical pickup device using the same.

Prior Art An optical pickup device for reading data or information recorded on an optical recording medium such as an optical disk includes a semiconductor laser as a light source, a lens for collimating the emitted light from the semiconductor laser, and an optical recording medium. In addition to an objective lens for forming a light spot on the top, a light receiving element for detecting the reflected light from the recording medium obtained through the objective lens, etc., depending on the focusing error detection method and tracking error detection method used, It is equipped with many optical elements such as gratings, polarizing beam splitters, and cylindrical lenses.

Since the optical pickup device is constructed by combining many of these optical elements, assembly work including optical axis adjustment etc. is quite complicated.

SUMMARY OF THE INVENTION OBJECTS OF THE INVENTION An object of the present invention is to provide an optical element having two functions: a lens function and another optical function.

This invention also. It is an object of the present invention to provide an optical pickup device that can simplify one assembly operation and downsize by using an optical element having two optical functions.

Arrangement 9 of the Invention Functions and Effects The optical element according to the present invention is characterized in that a composite grating pattern is formed on the substrate by 1ffi folding of two different types of grating patterns.

The grating is realized by a relief φ type (or corrugation type) that causes light diffraction by the protrusions and grooves on the substrate surface, or a refractive index distribution type that causes light diffraction by changing the refractive index of the substrate.

By setting one of the two types of grating patterns to be a Fresnel ψ lens φ pattern, a light condensing effect or a collimating effect (that is, a lens function) is realized. By making the other of the 2Fl type grating patterns a linear grating pattern with equal intervals.

This optical element realizes the above lens function and the light diffraction function of the linear grating.

By making one of the two types of grating patterns a Fresnel lens pattern and the other a non-uniformly spaced linear grating pattern, a lens function that focuses light on a single point and a cylindrical lens function that focuses light in a straight line can be achieved. Both lens functions can be achieved. Therefore, when parallel light is incident on this optical element, astigmatism occurs.

A dense grating with a period between 1 wavelength and 1/2 wavelength of the incident light causes Bragg diffraction in the incident light in a particular polarization direction. That is, the dense grating acts as a polarizing beam-splitter or filter. By setting one of the two types of grating patterns to be a Fresnel lens pattern and the other to be a high-density grating pattern, an optical element having a lens function and a polarizing beam splitter function is realized.

The optical element according to the present invention includes two types of ultra-high-density gratings that have a period of 1/2 or less of the wavelength of incident light and are orthogonal to each other. The thicknesses of these two types of ultra-high density gratings are set to be equal. The first type of ultra-high density grating has an envelope pattern of
The gratings are arranged to represent third grating shapes spaced apart by one or more wavelengths of incident light. The second type of ultra-high density grating is provided in a portion corresponding to the grooves of the third grating.

An ultra-high density grating with a period less than 1/2 of the wavelength of incident light has birefringence characteristics.

Therefore, the refractive index of the first type of ultra-high density grating in the direction perpendicular to the grating is equal to the refractive index of the second type of ultra-high density grating in the direction parallel to the grating.
When the duty ratio of a type of ultra-high density grating is determined, only light polarized in a direction parallel to the third grating is diffracted by the third grating.

Light with polarization components in other directions is transmitted. In this way, a polarizing beam splitter function is achieved.

By making the third grating a non-uniformly spaced grating, the function of a cylindrical lens is achieved.

The above-described optical element according to the present invention can be used in an optical pickup device. Since these optical elements have two types of optical functions, it is possible to reduce the size of the optical pickup device, and the number of assemblies of nine can be reduced to eight.

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIGS. 1 and 2 show a first embodiment of an optical element according to the invention.

On one surface of the substrate 10 that is transparent to incident light, a ring-like grating (
A Fresnel lens pattern 11 and a linear grating 12 are formed. These gratings 11 and 12 are of a relief type and consist of protrusions and grooves that are alternately repeated in one cycle.

For better clarity, a micro Fresnel lens and a linear grating are shown in Figures 3a and 3b, respectively. In FIG. 3a, the grating 11 of the micro-e Fresnel lens has a grating period that becomes smaller toward the outer periphery, and is blazed. The linear grating 11 is
As shown in Figure 3b, the steps with a constant period
It is of type. By overlapping these two types of gratings 11 and 12 with priority given to their grooves, the grating of the optical element 1 shown in FIGS. 1 and 2 (synthetic grating pattern) is obtained.
is configured. The period of the gratings 11 and 12 is equal to or longer than the wavelength λ of the incident light.

Needless to say, the Fresnel grating pattern may be shaped like a stem knob (rectangular), or the linear grating may be made into a blaze.

When collimated light enters this optical element 1, the incident light is diffracted by the Fresnel lens pattern 11, and the first-order diffracted light is focused at a focal position determined by the Fresnel lens pattern 11. This collimated incident light is also diffracted by the linear grating 12. Ignoring second-order or higher-order diffracted light by the linear grating 12, transmitted light (zero-order light) and ±1st-order diffracted light are considered. The light transmitted through the linear grating 12 is focused by the Fresnel lens pattern 11 as shown by the chain line in FIG. The +1st-order diffracted light and the 11th-order diffracted light of the linear grating I2 are also focused by the Fresnel lens pattern 11 at a different point from the transmitted light, as shown by broken lines in FIG. In this way, the optical element 1
acts to split the incident light into three light beams and to focus each of these three light beams on different points.

The intensity of the transmitted light and the ±1st-order diffracted light in the linear grating 12 is determined by the duty ratio a of this grating 11.
/Δ. Here, A is the period of the grating, and a is the width of the protruding portion. The +1st order or 11th order diffraction efficiency η is expressed by the following equation.

η-(4/π2) 51n2[(a/A) πl FIG. 4 shows a modification of the optical element 1. Here, a Fresnel lens pattern 11 and a linear grating 12 are formed on a substrate 10 so that their protrusions overlap.

FIG. 5 shows a configuration example of an optical pickup device constructed using the optical element 1 described above.

Laser light emitted from a semiconductor laser 8 serving as a light source enters the optical element 1 while spreading. The optical element 1 acts to split this laser light into three light beams and collimate each of them.

Since the laser beam emitted from the semiconductor laser 8 has an elliptical cross section, a shaping optical system consisting of a prism or the like is provided to shape the laser beam into a collimated beam with a circular cross section, or the Fresnel beam of the optical element 1 is Preferably, the lens pattern is oval.

Three light beams obtained from the optical element 1 pass through a beam splitter 15 and are focused by an objective lens 7 onto different positions on the optical disk 9. The three reflected lights from the optical disk 9 pass through the objective lens 7, are polarized by the beam splitter 15, and are focused by the light receiving lens 18 onto the three light receiving elements 17, 1111 and 19, respectively. The central light-receiving element 17 has four mutually independent light-receiving parts, and a read signal and a focusing error signal are generated from the output signal of this light-receiving element 17. A tracking error signal is generated from the output signals of the other two light receiving elements 18 and 19.

FIGS. 6 and 7 show a second embodiment of the invention.

In these figures, a Fresnel lens pattern 21 and nonuniformly spaced linear gratings 22 are overlaid on one surface of a transparent substrate 20 so that their grooves are prioritized.

Unequally spaced gratings 22 are used in this embodiment.

From one side of the substrate 20 to the other side, the grating interval (
period) becomes smaller. Another example of unevenly spaced gratings is one in which the grating spacing becomes narrower from one side toward the center.

On the other hand, there is a second example in which the grating interval becomes wider from both sides toward the center.

When parallel light enters such an optical element 2.

The light transmitted through the grating 22 is focused on its front axis by the Fresnel lens pattern 21, as shown by the chain line in FIG. The first-order diffracted light by the grating 22 is focused at a position offset from the optical axis of the Fresnel lens, as shown by the broken line in Figure 6, but astigmatism occurs in this focused light. . Unequally spaced grating 22
This is because the lens functions as a cylindrical lens and has different focal lengths in two directions perpendicular to the optical axis.

FIG. 8 shows the configuration of an optical pickup device including the above-mentioned optical element 2 as one component.

The emitted light from the semiconductor laser 8 enters the optical element 2, and the light (
0th order light) is collimated by the Fresnel lens pattern 21. Preferably, the Fresnel lens pattern is elliptical as described above. This collimated light is focused by the objective lens 7 and forms a light spot on the optical disk 9. The reflected light from the optical disk 9 is collimated through the objective lens 7 and enters the optical element 2 . A light-receiving element 27 is arranged at a position to receive the first-order diffracted light of this reflected light by the optical element 2 (first-order diffracted light by the unevenly spaced grating 22).

The light-receiving element 27 has four independent light-receiving parts, and a focusing error signal is created by the astigmatism method using the four light-receiving signals from the light-receiving element 27. That is, when the distance between the objective lens 7 and the optical disc 9 is equal to the focal length of the objective lens 7, the reflected light from the optical disc 9 is correctly collimated by the objective lens 7 and enters the optical element 2, so that the light reflected from the optical disc 9 is correctly collimated by the objective lens 7 and enters the optical element 2. A circular light spot is formed. If there is a change in the distance, the reflected light 9 will not be correctly collimated by the objective lens 7, and the optical element 2
Since the light is incident obliquely on the light receiving element 27, the light spot on the light receiving surface of the light receiving element 27 becomes elliptical.

The tracking error signal is created using a push-pull method (far-field method). That is, a tracking error signal is generated by dividing the four light receiving sections of the light receiving element 27 into two groups and taking the difference between the sum signals of each group. The read signal is generated by summing the output signals of the four light receiving sections.

In the above embodiment, a circular or elliptical grating
A composite grating pattern of an optical element is formed by a combination of a pattern and a linear grating pattern, but the shape of these patterns is arbitrary. For example, a grating with an arcuate pattern may be used instead of a linear grating.

9 to 11 show a third embodiment of the invention.

In these figures, when the wavelength of the incident light is λ, a high-density linear grating 32 with one period in the range of λ to λ/2 is superimposed on a Fresnel lens pattern 31 (III linear grating). A composite grating pattern is formed on the substrate 30 (the thickness of the grating 32 is modulated by the thickness of the Fresnel lens pattern). This is because the period of the high-density linear grating 32 is less than or equal to the wavelength λ.

This grating 32 does not cause light diffraction in the above-mentioned sense.

The optical element 3 has a high-density grating 32.

Used as a polarizing beam splitter with a focusing function. As shown in FIG. 12, the optical element 3 is arranged obliquely so that the Bragg diffraction condition is satisfied with respect to the incident light. Light polarized in the grating direction (longitudinal direction of the grating; Z direction) of the high-density grating 32 of the optical element 3 is diffracted by Bragg diffraction as shown by the broken line, and is focused by the Fresnel lens. Light in other polarization directions is simply focused by the Fresnel lens without undergoing Bragg diffraction, as shown by the dashed line. In this way, the optical element 3 has the function of separating incident light according to the polarization direction (polarization separation function) and focusing the light. Regarding the polarization separation effect of high-density gratings, N, G, M
oharas et al.

”o+rraction character
lcs of photoresistsurraee
-re+1er gras ngs, Appljed
Op mouth cs.

Vol, 23. No, 18.15 September
r 19g4. See pp3214-3220.

FIG. 13 shows an example in which the optical element 3 is applied to an optical pickup device that reads data from a magneto-optical disk.

The emitted light from the semiconductor laser 8 is collimated by the collimator lens 33, passes through the polarizing beam splitter 34, becomes linearly polarized light, and is sent to the magneto-optical disk 9A by the objective lens 7.
Focus the light upward. The plane of polarization of the linearly polarized light projected onto the magneto-optical disk 9A is rotated by magnetic recording on the surface of the disk 9A (err effect, parady effect).

The reflected light from the magneto-optical disk 9A is collimated by the objective lens 7.

The polarizing beam splitter 34 directs the light to the receiving optical system. The light receiving optical system is a 1/2 wavelength plate 35. Cylindrical lens 3B, optical element 3 and two light receiving elements 37.
Contains 38. The light receiving element 37 includes four independent light receiving sections. Astigmatism is produced by the cylindrical lens 36 and the Fresnel lens of the optical element 3, and the light is received by the light receiving element 37. Therefore, as described above, a focusing error signal based on the astigmatism method and a tracking error signal using the push-pull method are generated based on the output signal of the light receiving element 37.

On the other hand, the light Bragg diffracted by the optical element 3 is received by the light receiving element 38. Based on the difference between the output signals of the light receiving elements 37 and 38, a signal representing the rotation of the plane of polarization, that is, magnetically recorded data is obtained. Reference numeral 39 indicates a magnet (or electromagnet) used when recording data on the magneto-optical disk 9A.

14a to 14c show a method of manufacturing the optical element 1.degree. 2 or 3 described above.

First, a composite grating pattern of an optical element is formed by Ti beam lithography or other methods, and a stamper 14 is created using this as a model by a transfer method, an electroforming method, etc. (FIG. 14a).

Next, an ultraviolet curable transparent resin 13 is applied onto a transparent substrate 10 such as glass (Fig. 14b), and a stamper is placed on top of it.
Place 4. Then, while applying an appropriate pressure between the stamper 14 and the substrate 10, ultraviolet rays are irradiated from the substrate 10 side to harden the resin 13 (FIG. 14c). Stamper 14
Once removed, an optical element with a composite grating pattern formed on the substrate 10 is obtained. Both the substrate 10 and the composite grating pattern may be integrally resin molded.

FIG. 15 and FIG. 1B show an optical element according to a fourth embodiment of the invention.

In this optical element 4, ultra-high density equally spaced linear gratings 41 and 42 of the 2si type having a period of 1/2 or less of the wavelength λ of the incident light are formed on a substrate 40. 1st
The ultra-high-density gratings 41 are provided at appropriate intervals, and their envelopes are ji
3 represents a non-uniformly spaced linear grating. In this embodiment, the third grating 43 is an irregularly spaced grating, and its minimum interval (period) is equal to or greater than the wavelength λ of the incident light. A second ultra-high density grating 42 is provided in a portion corresponding to the groove of the third grating 43, and this second ultra-high density grating 42 is orthogonal to the first ultra-high density grating 41. . Both ultra-high density gratings 41 and 42 have the same thickness (depth).

An ultra-high-density grating with a period of 1/2 or less of the wavelength λ of the incident light does not diffract the incident light (the incident light is transmitted as is), but exhibits birefringence characteristics with respect to the incident light. It exhibits a different refractive index depending on the polarization direction of the light.

Let the period of the first ultra-high density grating 41 be A, and the width of the protrusions be al. Second ultra-high density grating 42
The period of Δ2. Let the width of the protrusion be a2. The duty ratios of these ultra-high density gratings 41 and 42 are expressed as a/Δ and a2/A2, respectively. Although the ultra-high density 1 degree grating 41,42 exhibits birefringent properties,
The refractive index n for light polarized in a direction parallel to these gratings (parallel to the longitudinal direction of the ridges of the grating) is different from the refractive index nA for light polarized in a direction perpendicular to the gratings, Moreover, these refractive indexes n, , nm are given by the duty ratio k as shown in FIG.
It changes depending on. In FIG. 18, no is the refractive index of the grating medium, and 1 is the refractive index of air. When the duty ratio is g, the refractive index n in the direction parallel to the grating ((1)) is equal to the refractive index ni (intestine) in the direction perpendicular to the grating when the duty ratio is m, which is the same value nb
shows.

The refractive indexes nz and n5 of the ultra-high density grating 41 are represented by a subscript 1, and the refractive indices nl and n of the ultra-high density grating 42 are represented by a subscript 2. n15-n2. The duty ratio of these ultra-high density gratings 41.42 (grating 41
The duty ratio of is m.

When the duty ratio of the grating 42 determines p),
As shown in FIG. 17a, for incident light with polarization perpendicular to the direction of the grating 41 (parallel to the direction of the grating 42), this optical element 4 becomes a plate-like body with a -like refractive index. Therefore, this incident light passes through the optical element 4 and no diffraction phenomenon occurs. If the duty ratio of the grating is determined as above, from Fig. 18 * ' +
7”” n , n 2j−n (n ≠ m
), and for incident light with polarization parallel to the Ca C direction of the grating 41 (perpendicular to the direction of the grating 42), the optical element 4 acts as a grating whose refractive index changes with the period of the third grating 43. Become. Therefore, such incident light is diffracted by the grating 43, as shown in FIG. 17b.

In this way, the optical element 4 has the function of a polarizing beam splitter. Furthermore, since the period of the grating 43 changes in its width direction, the optical element 4 has a function equivalent to that of a cylindrical grating lens.

The refractive index difference between the convex stripes and the concave grooves of the grating 43 is n −
n, the maximum diffraction efficiency (first-order light a
The grating thickness d (first
(see Figure 6) is given by d-λ/2<n-n) a
C. Can be done. FIG. 19 shows the diffraction efficiency of first-order diffracted light (shown by a solid line) and the transmission efficiency of zero-order light (shown by a broken line) with respect to the polarization angle of incident light. The polarization angle of the incident light shown in FIG. 17a is set to 0.

- For example, when grating 41.42 is made using n-1,57 ultraviolet curing resin, 1-0.4
1. When m-0,67, n b -1,27. Also, n ”” 1-41+ n -1, 15, and the thickness a at this time is
C is d −1,52 μm. The wavelength of the incident light is λ-0.
It is 78 μm.

Such an optical element 4, as shown in FIG. 20, can be used as an optical pickup device for a magneto-optical disk. In FIG. 20, the same components as those shown in FIG. 13 are given the same reference numerals. In place of the cylindrical lens 36 and optical element 3 shown in FIG. 13, an optical element 4 and condensing lenses 47 and 48 are arranged. Of the reflected light from the magneto-optical disk 9A, the light diffracted by the optical element 4 passes through the condenser lens 47 and enters the light receiving element 37,
A focusing error signal and a tracking error signal are generated based on the output of the light receiving element 37. The light transmitted through the optical element 4 passes through the condenser lens 48 and enters the light receiving element 38 . A read signal is generated based on the output signals of the light receiving elements 37 and 38.

21a to 21c show a method of manufacturing the optical element 4. FIG. A resist or other medium 44 with a high etching rate by reactive ion etching (or ion beam etching) is coated thickly on the substrate 40, and an electron beam φ with a low etching rate is applied thereon.
A thin layer of resist 45 is applied (FIG. 21a). Ultra-high density gratings corresponding to the gratings 41 and 42 are formed on the electron beam resist 45 by electron beam lithography (FIG. 21b). Finally, the medium 44 is etched by reactive ion etching using the ultra-high density grating made of electron beam resist as a mask (Figure m21c). The thickness d of the grating is controlled by the thickness of the resist 45 and medium 44.

It is also possible to produce a stamper using the optical element thus produced as a prototype, and use this stamper to duplicate the optical element 4.

In the above embodiments, a cylindrical grating lens is shown as the third grating, but other types of gratings, such as equally spaced gratings, circular arc gratings, and other arbitrary shapes may be employed.

[Brief explanation of the drawing]

FIG. 1 is a plan view showing an optical element according to a first embodiment of the present invention. FIG. 2 is a sectional view taken along the line ■--■ in FIG. 1. Figure 3a is a cross-sectional view of the micro Fresnel lens;
Figure b is a cross-sectional view of the equally spaced grating. FIG. 4 is a sectional view showing a modification of the optical element. FIG. 5 shows an optical configuration of an optical pickup device using the optical element shown in FIG. 1. FIG. 6 is a perspective view showing an optical element according to a second embodiment of the invention. FIG. 7 is an enlarged sectional view taken along the line ■--■ in FIG. 6. FIG. 8 shows the optical configuration of an optical pickup device using the optical element shown in FIG. 6. FIG. 9 is a plan view showing an optical element according to a third embodiment of the invention. FIG. 1θ is a sectional view taken along the line X--X in FIG. 9. FIG. 11 is an enlarged view of a portion of FIG. 1O. FIG. 12 shows the polarization separation effect of the optical element according to the third embodiment. FIG. 13 shows the optical configuration of an optical pickup device using the optical element shown in FIG. 9. 14a to 14c illustrate a method of manufacturing the above-mentioned optical element. FIG. 15 is a perspective view showing an optical element according to a fourth embodiment of the present invention. FIG. 16 is an enlarged view of a part of FIG. 15. FIGS. 17a and 17b are for explaining the function of the optical element shown in FIG. 15. FIG. 18 is a graph showing the relationship between duty ratio and refractive index. FIG. 19 is a graph showing the relationship between the incident polarization angle and the diffraction efficiency. FIG. 20 shows the optical configuration of a first pickup device using the optical element shown in FIG. 15. 21a to 21c show a method of manufacturing the optical element shown in FIG. 15. 1.2, 3.4... optical element. 9...Optical disc. 9A...Magneto-optical disk. 10, 20.30.40...Substrate. 11, 21.31... Fresnel Emperor Shinzuken pattern. 12... Equally spaced linear grating. 22... Unequally spaced linear grating. 32...High density grating. 41, 42...Ultra high density grating. 43...Third grating.

Claims (13)

[Claims] (1) An optical element in which a composite grating pattern formed by superimposing two different types of grating patterns is formed on a substrate. (2) Claim (1), wherein one of the two types of grating patterns is a Fresnel lens pattern.
The optical element described in . (3) The optical element according to claim (2), wherein the other of the two types of grating patterns is a linear grating pattern with equal intervals. (4) the other of the two types of grating patterns is a linear grating pattern with uneven intervals;
The optical element according to claim (2). (5) One of the two types of grating patterns has a spacing greater than the wavelength of the incident light, and the other has a high-density grating pattern with a period between 1 wavelength and 1/2 wavelength of the incident light. The optical element according to claim 1, which is a pattern. (6) The optical element according to claim 5, wherein one of the two types of grating patterns is a Fresnel lens pattern. (7) It has two types of ultra-high-density gratings that have a period of 1/2 or less of the wavelength of the incident light and are orthogonal to each other, and the first type of ultra-high-density grating has an interval of at least one wavelength of the incident light. are arranged to form an envelope pattern representing a third grating of the second type, a second type of ultra-high density grating is provided in a portion corresponding to the grooves of the third grating, and a second type of ultra-high density grating is provided in a portion corresponding to the grooves of the third grating; An optical element in which the thickness of a density grating and a second type of ultra-high density grating are set to be equal. (8) The refractive index of the first type of ultra-high density grating in the direction perpendicular to the grating is equal to the refractive index of the second type of ultra-high density grating in the direction parallel to the grating. 8. The optical element according to claim 7, wherein the duty ratio of the ultra-high density grating is determined. (9) The optical element according to claim 7, wherein the third grating represented by the envelope pattern is an unevenly spaced grating. (10) A Fresnel lens pattern and an equally spaced grating pattern are used as optical elements for splitting the laser light from the laser light source into three light beams, collimating these light beams, and making them incident on the objective lens. An optical pickup device that uses an optical element in which a composite grating pattern formed by overlapping is formed on a substrate. (11) A composite grating constructed by superimposing a Fresnel lens pattern and an unevenly spaced grating pattern as an optical element for guiding reflected light from an optical recording medium collimated through an objective lens to a light receiving element.・An optical pickup device that uses an optical element with a pattern formed on a substrate. (12) A Fresnel lens pattern and a high-density grating with a period between 1 wavelength and 1/2 wavelength of the reflected light as one of the optical elements for guiding the reflected light from the magneto-optical recording medium to the light receiving element. - An optical pickup device that uses an optical element in which a composite grating pattern formed by superimposing patterns on a substrate is formed. (13) As one of the optical elements for guiding the reflected light from the magneto-optical recording medium to the light-receiving element, two types of ultra-high-density gratings, which have a period less than 1/2 of the wavelength of the incident light and are orthogonal to each other, are used. the first type of ultra-dense gratings are arranged to form an envelope pattern representing third gratings spaced apart by one or more wavelengths of incident light, and the second type of ultra-dense gratings are , provided in a portion corresponding to the groove of the third grating, the thickness of the first type of ultra-high density grating and the second type of ultra-high density grating are set equal, and the thickness of the first type of ultra-high density grating is set equal to The duty ratio of these two types of ultra-high-density gratings is set such that the refractive index in the direction perpendicular to the grating in the high-density grating and the refractive index in the direction parallel to the grating in the second type of ultra-high-density grating are equal. is determined, and the third grating represented by the envelope pattern is an unevenly spaced grating.